Many wave forms may be digitized. The waveforms may be sampled or measured over regions, and values generated for the regions based upon the measurements. The values may be converted to binary numbers by grouping them into ranges, and representing the ranges by digital numbers. For example, sound waves may be digitized by measuring the magnitude of the waves at intervals and converting the measurements to binary numbers. Similarly, an image may be digitized by capturing the irradiance produced by the surface of the image and measuring the irradiance over small areas called pixels.
One type of digital imaging is medical imaging. Waves may be generated which pass through a human body or a tissue sample. Digital data representing images of the interior of the sample may be created by measuring the waves and performing calculations based upon the measurements. In some cases, the machine doing the measuring also creates the waves. For example, X-ray machines and CT scans produce X-rays which penetrate the body. Similarly, ultrasound machines produce high-intensity sound waves which penetrate the body. In other cases, ingested matter produces the waves. For example, ingested radioactive material may decay, producing gamma waves or other radioactive waves.
Television is another kind of digital imaging. The images may be broadcast interleaved. An image may be divided into lines. For example, standard definition television displays consist of 525 lines. In an interleaved broadcast, the image is broadcast in halves or fields. Each field consists of every other line, and the two fields together contain all of the lines in the image on the display. For example, one field may contain the odd-numbered lines and the next field may contain the even-numbered lines.
The digital data may be presented to reproduce the original wave form. For example, digital audio may be converted back to audio waves. Pixels may be displayed in a monitor or television screen. The quality of reproduction of a digital wave form during the presentation of the digital data may depend on the resolution, the number of data points. Two existing methods to improve resolution may be ineffective. The first method increases the data by increasing the number of samples or measurements taken. Samples may be taken more frequently, in the case of sound, or over smaller areas in the case of images. More generally, the region over which the wave form is sampled may be decreased. Increasing the samples may prove expensive. The smaller samples may require more sophisticated equipment to take more frequent samples or samples over small physical regions. Further, the additional sampling produces additional data. Working with the additional data may require additional storage, more powerful processing capabilities, and more broadband to transport the data. In the case of medical imaging, the increased resolution may require more intense or longer application of radiation, which may harm patients.
A second method may use computation to interpolate calculated points between the measured data points. The source input points (A, B, C, . . . ) are retained in the output and intervening point values (ab, bc, . . . ) are interpolated using a variety of techniques from simple linear interpolation, to more complex mathematical curve fitting algorithms. In two-dimensional applications (such as image processing), the computations may use interpolation along both axes to better approximate intervening data point (pixel) values. This interpolation is carried out along both axes concurrently to provide a best surface fit to the scaled data.
Common two-dimensional interpolation algorithms include nearest neighbor, bilinear interpolation, bicubic interpolation, spline curve fitting, and sparse point filtering. Various curve approximation techniques (bicubic, Catmull-Rom, etc.) are used in spline approaches. Windowed filtering techniques apply various filters such as Gaussian, or sinc based functions (Lanczos filters). Most of the effort in computational approaches may be directed to improvements in specific curve fitting algorithms in spline approaches, and to filter design in spatial filtering approaches. These concurrent interpolation approaches may be extended to three-dimensional applications by adjusting weighting functions, curve fitting algorithms and spatial filters.
The quality (accuracy) of the scaled output is proportional to the suitability of the specific interpolation algorithm applied to the input data points to arrive at intervening point values. Higher quality results may require more sophisticated interpolation methods (splines and spatial filtering) and may thus increase computation complexity. In many applications, such as digital cameras, the quality of the scaled output may be sacrificed in order to reduce computational loads.